Three-dimensional equilibrium structures of rotating and self-gravitating gas clouds and its application to astrophysics

利用Hachisu的自洽场代码，我们构建了大量轴对称的、平衡的旋转多向气体云模型，允许许多不同的角动量分布。通过仔细研究生成的平衡序列，我们推导出了旋转气体云的几个重要的一般性质。对于角动量分布类似于麦克劳林球体的云，对于N = 0和N = 3之间的所有多向指数，在T/|W|值介于0.44和0.45之间时，环形平衡序列从球体序列中分叉。这里，T是旋转动能，W是云的重力势能。这表明，在线性扰动状态下，对于大范围的多向指数，动力环模不稳定性几乎相同的值为T/|W|。此外，我们还证明了T/|W| > 0.41的中心凝聚平衡构型在非线性环境下对环的形成不稳定。由于这些高T/|W|系统几乎肯定不稳定到非轴对称的jean型不稳定，我们假设环模和扇形模不稳定的耦合将导致所有T/|W| > 0.41的云经历动态破碎。利用我们的非线性环形成分析，我们可以精确地预测在什么初始条件下初始轴对称坍缩云经历破碎。对于大多数其他选择的角动量分布，发生非线性环形成和非轴对称jeans型不稳定性发生的T/|W|的确切值有所变化，但定性行为保持不变。

Using Hachisu's self-consistent field code, we have constructed a large number of axisymmetric, equilibrium models of rotating polytropic gas clouds, allowing for a number of different angular momentum distributions. By carefully studying the generated equilibrium sequences, we have deduced several important general properties of rotating gas clouds.For clouds having an angular momentum distribution like that of Maclaurin spheroids, a toroidal equilibrium sequence bifurcates from the spheroidal sequence at a value of T/|W| somewhere between 0.44 and 0.45 for all polytropic indices between N = 0 and N = 3. Here, T is the rotational kinetic energy and W is the gravitational potential energy of the cloud. This suggests that a dynamical ring mode instability sets in at almost the same value of T/|W| for a wide range of polytropic indices in the linear perturbation regime.In addition, we show that centrally condensed equilibrium configurations with T/|W| > 0.41 are unstable to ring-formation in the nonlinear regime. Since these high T/|W| systems are almost certainly unstable to a nonaxisymmetric Jeans-type instability, we hypothesize that the coupling of the ring mode and the sector mode instability will cause all clouds with T/|W| > 0.41 to undergo dynamical fragmentation. Utilizing our nonlinear ring formation analysis, we can precisely predict under what initial conditions initially axisymmetric collapsing clouds experience fragmentation. For most other chosen angular momentum distributions, the exact value of T/|W| at which nonlinear ring formation occurs and at which the nonaxisymmetric Jeans-type instability sets in changes somewhat, but the qualitative behavior remains the same.